The problem
ACC reacts only to measured gap and relative speed, so disturbances amplify along a line of vehicles unless time gaps are large, which limits road capacity. Cooperative ACC adds the preceding vehicle's acceleration over V2V communication, allowing shorter gaps with string stability. But wireless communication brings delay and packet loss, and a platoon must degrade safely when messages are lost. Designing CACC that is string stable under realistic communication is a core research topic for connected vehicles and freight platooning.
Objectives
- Model a platoon of heterogeneous vehicles with actuator lags and sensor delay.
- Design ACC and CACC controllers with constant time-gap spacing policies.
- Analyse string stability in the frequency domain as a function of time gap and communication delay.
- Simulate communication with delay and packet loss and design a graceful degradation strategy.
- Evaluate the minimum string-stable time gap, safety margins and robustness in co-simulation.
What you need
Tools and toolboxes
- MATLAB with Control System Toolbox — Transfer functions, frequency responses and H-infinity norm calculation for string stability analysis.
- Simulink — Time-domain platoon simulation with vehicle models, controllers and a communication delay and loss model.
- Stateflow — Platoon modes: join, follow with CACC, degraded ACC on communication loss and leave.
- OMNeT++ with Veins and Plexe (optional) — Open-source network and platooning co-simulation with SUMO for realistic V2V message delivery.
- Model Predictive Control Toolbox (optional) — A distributed MPC variant for comparison with linear CACC.
Software
- MATLAB R2023b or later
- Control System Toolbox
- Simulink
- Stateflow
- OMNeT++, Veins, Plexe and SUMO (optional)
Extra parts and data
None beyond the software above.
Key concepts
- String stability
- A platoon is string stable if disturbances such as a braking lead vehicle do not grow as they travel down the line. In the frequency domain, the transfer function from one vehicle's motion to the next must have gain not greater than one at all frequencies.
- Feedforward over V2V
- CACC adds the preceding vehicle's commanded or measured acceleration as a feedforward term, so the follower can react before the gap changes.
- Communication delay and loss
- V2V messages arrive after a delay and some are lost. Delay reduces the benefit of feedforward, and loss requires a fallback, such as estimating the predecessor's acceleration or reverting to ACC.
- Information flow topology
- Which vehicles each follower receives data from: predecessor only, predecessor and leader, or several vehicles ahead. Topology affects string stability and robustness.
Step-by-step guide
- 1
Frame the research questions
State the questions: what is the minimum string-stable time gap for CACC as a function of communication delay, packet loss and vehicle heterogeneity, and how well does a degradation strategy maintain safety when communication fails? Define metrics: minimum string-stable time gap, peak spacing error amplification along the platoon, minimum gap in emergency braking and time spent in degraded mode. Agree the scope, such as passenger cars or light commercial vehicles, with your guide.
Checkpoint: A written research plan with questions, metrics and scope.
- 2
Model the vehicles
Model each vehicle with longitudinal dynamics and a first-order lag between commanded and actual acceleration, with different lags and masses for heterogeneous platoons. Add a radar measurement of gap and relative speed with small noise and delay. Build a platoon of, for example, eight vehicles in Simulink with a parameterised leader speed profile including steps, sine waves and emergency braking.
Checkpoint: An eight-vehicle platoon that runs with any chosen set of vehicle parameters.
- 3
Design the ACC baseline and analyse it
Design a constant time-gap ACC with feedback on spacing error and relative speed. Derive the transfer function from predecessor to follower acceleration and compute its peak gain over frequency with Control System Toolbox functions such as bode and hinfnorm. Find the minimum time gap for string stability as a function of actuator lag and confirm it in time-domain simulation. Repeat for two or three gain sets to show how gains shift the boundary.
Checkpoint: Analytical and simulated minimum string-stable time gaps for ACC that agree.
- 4
Design CACC and analyse it
Add a feedforward term using the predecessor's acceleration received over V2V, delayed by the communication delay θ. Derive the transfer function including the delay term and compute the minimum string-stable time gap as a function of θ and actuator lag. Plot this boundary. Expect CACC to allow much shorter gaps than ACC at small delays, with the advantage shrinking as delay grows.
Checkpoint: A plot of minimum string-stable time gap against communication delay for CACC and ACC.
- 5
Add a communication model
In Simulink, model V2V messages sent at 10 Hz with configurable delay, jitter and packet loss, either random or in bursts. Hold the last received value between messages and track message age. Optionally run the same experiments in OMNeT++ with Veins and Plexe, which simulate IEEE 802.11p-style channels and platooning on SUMO traffic, to check that results hold with a network simulator.
Checkpoint: Logged message delays and losses that match the configured distributions.
- 6
Design the degradation strategy
When messages are lost, options include estimating the predecessor's acceleration from radar range-rate, increasing the time gap smoothly, and reverting to ACC after a timeout. Implement these in a Stateflow mode manager with join, CACC follow, degraded and leave states. Design the gap increase so the vehicle opens the gap without harsh braking. Test the transitions with scripted communication failures.
Checkpoint: Stateflow runs where a communication loss leads to a smooth gap increase and ACC fallback without unsafe gaps.
- 7
Test emergency braking
Run emergency braking of the leader at high deceleration with CACC at short gaps, with nominal communication and with a burst of lost messages at the start of braking. Record minimum gaps for every follower. Check whether any follower would collide and how much margin remains. This tests the worst case for short-gap platooning and is essential for any safety argument.
Checkpoint: Minimum gap for every follower in emergency braking under nominal and lossy communication.
- 8
Study heterogeneity and topology
Repeat the string stability analysis and simulations with mixed vehicle lags and masses, for example a heavy van in a line of cars. Compare predecessor-only topology with predecessor-plus-leader topology. Record the minimum string-stable time gap and emergency braking margins. Heterogeneity often forces larger gaps or per-vehicle tuning, which is a practical constraint for real platoons. Note which vehicle position in the platoon is most sensitive to a heavier vehicle ahead.
Checkpoint: A table of minimum time gap and braking margins for each heterogeneity case and topology.
- 9
Run the parameter study
Sweep communication delay (0 to 300 ms), packet loss (0 to 50 per cent, random and bursty), time gap and platoon length. For each combination, run disturbance tests and measure spacing error amplification, string stability in the time domain and safety margins. Present results as maps of safe and string-stable operating regions, which are more useful than single numbers. Run each combination over several random loss patterns and report the spread.
Checkpoint: Operating-region maps of time gap against delay and loss for CACC with degradation.
- 10
Compare with distributed MPC (optional)
Implement a distributed MPC follower that uses received predecessor plans over a short horizon, with constraints on acceleration and minimum gap. Compare its string stability, comfort and computation with linear CACC on the same tests. This comparison is often requested by examiners and shows whether the extra complexity pays off under realistic communication. Keep vehicle models, communication settings and scenarios identical so only the controller differs, and record solver time per step for each follower.
Checkpoint: A comparison table of linear CACC and distributed MPC on stability, comfort and computation.
- 11
Write up the research
Present the models, analytical string stability results, communication model, degradation strategy, emergency braking tests, heterogeneity and topology studies and operating-region maps. Clearly separate analytical results from simulation results and show where they agree. Discuss limits of simulation and assumptions about the communication channel. Release models and scripts to support reproduction. Include the derivations in an appendix so each transfer function can be checked, and summarise the recommended time gaps for typical delay levels in one table.
Checkpoint: Thesis chapters with analytical and simulation results, operating-region maps and released code.
Testing & validation
- Analytical and simulated minimum string-stable time gaps agree for ACC and CACC.
- Minimum time gap against communication delay and packet loss.
- Minimum gaps in emergency braking with nominal and lossy communication.
- Effect of vehicle heterogeneity and information topology.
- Smooth and safe transitions in the degradation mode manager.
Expected results
A CACC design with analytically and numerically verified string stability, a graceful degradation strategy and operating-region maps showing safe time gaps under realistic communication delay and loss.
Research angle for your PhD
Research questions: how do communication delay, bursty packet loss and vehicle heterogeneity jointly set the minimum safe, string-stable time gap for CACC, and how effectively does a graceful degradation strategy preserve safety during communication failures? Metrics: minimum string-stable time gap, spacing error amplification, emergency braking margins and time in degraded mode. Baselines: ACC and predecessor-only CACC. Operating-region maps combining analysis and network co-simulation, with released models, are a solid basis for journal or conference papers.
Take it further
- Add security checks against false acceleration messages and measure their effect.
- Use preview of the leader's planned speed for energy-efficient platooning.
- Study mixed platoons with human-driven vehicles between CACC vehicles.
- Implement the CACC on two scale-model vehicles in a supervised lab setting.
Viva and review questions
Why can CACC use shorter time gaps than ACC?
The feedforward of the predecessor's acceleration lets the follower react before the gap changes, which reduces amplification of disturbances along the platoon.
How does communication delay affect string stability?
Delay makes the feedforward arrive late, so its benefit shrinks; beyond a certain delay the minimum string-stable time gap approaches that of ACC.
What happens when V2V messages are lost?
The follower estimates the predecessor's acceleration or opens the gap smoothly and reverts to ACC after a timeout, so the platoon stays safe without communication.
How did you check string stability?
Analytically, by checking that the peak gain of the predecessor-to-follower transfer function is at most one, and in simulation by confirming disturbances do not grow along the platoon.
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